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The linear and non-flexible nature of deep convolutional models makes themvulnerable to carefully crafted adversarial perturbations. To tackle thisproblem, we propose a non-linear radial basis convolutional feature mapping bylearning a Mahalanobis-like distance function. Our method then maps theconvolutional features onto a linearly well-separated manifold, which preventssmall adversarial perturbations from forcing a sample to cross the decisionboundary. We test the proposed method on three publicly available imageclassification and segmentation datasets namely, MNIST, ISBI ISIC 2017 skinlesion segmentation, and NIH Chest X-Ray-14. We evaluate the robustness of ourmethod to different gradient (targeted and untargeted) and non-gradient basedattacks and compare it to several non-gradient masking defense strategies. Ourresults demonstrate that the proposed method can increase the resilience ofdeep convolutional neural networks to adversarial perturbations withoutaccuracy drop on clean data.

A Kernelized Manifold Mapping to Diminish the Effect of Adversarial Perturbations